Long-term dynamics of the coupled suspension bridge system

In this paper we study the long-term dynamics of a nonlinear suspension bridge system. The road bed and the main cable are modeled as a nonlinear beam and a vibrating string, respectively, and their coupling is carried out by one--sided springs. First, we scrutinize the set of stationary solutions, which turns out to be nontrivial when the axial load exceeds some critical value. Then, we prove the existence of a bounded global attractor of optimal regularity and we give its characterization in terms of the steady states of the problem.